We also demonstrate the monotonicity of quantum coherences of the squeezed state and the entanglement state in lossy and noisy channels as shown in Fig. 2 and 3, respectively. The quantum coherences of these two Gaussian states are decreasing with the increase of loss and noise in quantum channels, which is because the lossy and noisy channels are all incoherent operations and quantum coherence will decrease under incoherent operations [1]}, [2]}. The physical reason for the robustness of quantum coherences of these Gaussian states in a noisy channel is that the proportion of quantum coherence is decreased when it is mixed with thermal noise, but the quantum coherence disappears completely only when infinite thermal noise is involved.
